The wave gear device was invented by C. W. Musser (Patent Document 1). Since then, wave gear devices have been the subject of a variety of inventions made by other researchers including the inventor of the present invention. Even with regards specifically to tooth profile, the inventions are diverse. For example, the inventor of the present invention has proposed using an involute tooth profile as the basic tooth profile in Patent document 2; and proposed a method for designing a tooth profile, where a technique is used in which meshing of a rigid internally toothed gear and a flexible externally toothed gear is rack-approximated in order to obtain an addendum tooth profile for the two gears, which contact each other over a wide range, in Patent Documents 3 and 4.
Typically, a wave gear device has an annular rigid internally toothed gear, a flexible externally toothed gear disposed coaxially on the inner side of the rigid internally toothed gear, and a wave generator fitted on the inner side of the flexible externally toothed gear. The flexible externally toothed gear is provided with a flexible cylindrical barrel part, a diaphragm extending in a radial direction from a rear edge of the cylindrical barrel part, and external teeth formed on an external circumferential surface portion of the cylindrical barrel part towards a front-edge opening.
The flexible externally toothed gear is deflected into an ellipsoidal shape by the wave generator, and caused to mesh with the rigid internally toothed gear at both end parts in the direction of the major axis of the ellipsoid. The amount of deflection of the external teeth of the flexible externally toothed gear deflected into an ellipsoidal shape increases from an external-tooth inner edge on the diaphragm side to the external-tooth outer edge on the front-end opening side along the tooth trace direction of the external teeth, the amount of deflection being substantially proportional with respect to the distance from the diaphragm. Each portion of the toothed parts of the flexible externally toothed gear is repeatedly deflected radially outward and inward as the wave generator rotates. This deflecting action of the teeth of the flexible externally toothed gear is known as coning.
When the flexible externally toothed gear is deformed into an ellipsoidal shape by the wave generator, a rim-neutral circle of the external teeth of the flexible externally toothed gear is deformed into an ellipsoidal rim-neutral curve. Taking w to be the amount of radial deflection in relation to the rim-neutral circle before deformation in the longitudinal position of the neutral curve of the rim, the value obtained by dividing the radius of the rim-neutral circle by the reduction ratio of the wave gear device is called the regular (standard) deflection amount wo, and the ratio of these values (w/wo) is called the deviation factor κ. Deflection of the regular deflection amount wo is called “zero-deviation deflection,” deflection in an amount larger than the regular deflection amount wo (κ>1) is called “positive-deviation deflection,” and deflection in an amount smaller than the regular deflection amount wo (κ<1) is called “negative-deviation deflection.” Taking m to be the module of the flexible externally toothed gear and n to be the difference in the number of teeth between the flexible externally toothed gear and the rigid internally toothed gear (n being a positive integer), the amount of deflection w is 2 κmn.
In Patent Document 5, the present inventor has proposed a wave gear device provided with a tooth profile capable of continuous meshing, with consideration being given to coning of the teeth of the flexible externally toothed gear. The wave gear device proposed in Patent Document 5 shall be described next.
An arbitrary position in the tooth-trace direction of a cross section perpendicular to the axis of the flexible externally toothed gear is defined as a main cross-section, and the deflection of the flexible externally toothed gear at the main cross-section is set to zero-deviation deflection (κ=1). The meshing of the flexible externally toothed gear and the rigid internally toothed gear is approximated by rack meshing. The movement trajectories of a tooth of the flexible externally toothed gear relative to a tooth of the rigid internally toothed gear as the wave generator rotates is determined for an axially perpendicular cross-section at each position, including the main cross-section, along the flexible externally toothed gear in the tooth trace direction. There is determined a first similarity curve, in which a curve portion extending from a top point to a next bottom point of a zero-deviation-deflection movement trajectory obtained on the main cross-section is scaled down λ-fold (where λ<1) using the bottom point as the center of similarity. The first similarity curve is used as a basic tooth profile of the addendum of the rigid internally toothed gear.
A second similarity curve is determined in which a curve obtained by rotating the first similarity curve by 180 degrees about an endpoint of the first similarity curve is scaled up (1−λ)/λ-fold using the endpoint as the center of similarity. The second similarity curve is used as a basic tooth profile of the addendum of the flexible externally toothed gear.
Profile shifting is applied to tooth-profile portions on either side in the tooth-trace direction of the external teeth of the flexible externally toothed gear so that both a first movement trajectory and a second movement trajectory describe curves that are tangent to the bottom of the zero-deviation deflection movement trajectory on the main cross-section, the first movement trajectory being obtained for each axially perpendicular cross-section in which there occurs negative-deviation deflection (deviation factor κ<1) farther toward the diaphragm than the main cross-section of the external tooth of the flexible externally toothed gear, and the second movement trajectory being obtained in each axially perpendicular cross-section in which there occurs positive-deviation deflection (deviation factor κ>1) farther toward the front-end opening than the main cross-section of the external tooth of the flexible externally toothed gear.
In a wave gear device having a tooth profile formed as described above, it is possible to obtain effective meshing over the range of the tooth trace extending from the main cross-section to the outside end of the outer teeth and the range of the tooth trace extending from the main cross-section to the inside end of the outer teeth, centered around continuous tooth-profile meshing extending over a wide range on the main cross-section. It is thereby possible to transmit a larger torque than with a conventional wave gear device in which meshing occurs over a narrower tooth trace range.